To overcome the limitations of triangle and point based surfaces several authors have recently investigated surface representations that are based on higher order primitives. Among these are MPU, SLIM surfaces, dynamic skin surfaces and higher order iso-surfaces. Up to now these representations were not suitable for interactive applications because of the lack of an efficient rendering algorithm. In this paper we close this gap for implicit surface representations of degree two by developing highly optimized GPU implementations of the raycasting algorithm. We investigate techniques for fast incremental raycasting and cover per fragment and per quadric backface culling. We apply the approaches to the rendering of SLIM surfaces, quadratic iso-surfaces over tetrahedral meshes and bilinear quadrilaterals. Compared to triangle based surface approximations of similar geometric error we achieve only slightly lower frame rates but with much higher visual quality due to the quadratic approximation power of the underlying surfaces

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